External sources of knowledge and value invention in logic programming

Abstract

The issue of value invention in logic programming embraces many scenarios, such as logic programming with function symbols, object oriented logic languages, inter-operability with external sources of knowledge, or set unification. This work introduces a framework embedding value invention in a general context. The class of programs having a suitable (but, in general, not decidable) 'finite grounding property' is identified, and the class of 'value invention restricted' programs is introduced. Value invention restricted programs have the finite grounding property and can be decided in polynomial time. They are a very large polynomially decidable class having this property, when no assumption can be made about the nature of invented values (while this latter is the case in the specific literature about logic programming with function symbols). Relationships with existing formalisms are eventually discussed, and the implementation of a system supporting the class of such programs is described.

The Intelligent Grounder of DLV

“…Indeed, it incorporates many algorithms for improving the performance (see Section 5), including database optimization strategies and parallel evaluation techniques allowing for dealing with data-intensive applications. Moreover, it is endowed with a number of mechanisms that meet the requirement of real-world applications and make its usage feasible in practice: database interoperability is possible by means of an ODBC interface [25,38] which allows for both importing input data from and exporting answer set data to an external database; plugin functions [4] provide a framework for integrating application specific functions in logic rules and dealing with external sources of computation; non-ground queries allow for advanced reasoning.…”

Towards a Type Discipline for Answer Set Programming

“…Any non-trivial type signature is a source of infinity. We draw our inspiration from the way in which [5] deals with computable functions. We view type instantiation and grounding of individual variables as two separate phases.…”

“…Thus, the problem of grounding a clause in presence of predicates and operations defined in the grounding structure G is reduced to a constraint solving problem over G. The class of the groundable programs depends both on the grounding strategy and on the class of the constraints that the grounder can solve. For example, we could reconstruct value invention as treated in [5] in terms of programs that guarantee the solvability of a special class of constraints.…”

“…In this section we provide the bare minimum of definitions of the syntax and semantics of DLV [16] (disjunctive Datalog) and we briefly describe its extension with functions [5].…”

“…6 for a detailed discussion -it is safe to say that types have never been integrated into ASP; in fact the above papers do not consider a many-sorted model theory, nor any form of parametric polymorphism. The present paper introduces static type-checking in DLV-Complex [5], an extension of DLV with uninterpreted function symbols -hence we are leaving the comfort of Datalog -as well with external types and predicates requiring an oracle to be computable. In other terms, one may exploit external sources of knowledge.…”